Although respiratory rate is an important vital sign for early detection of deterioration, on general wards it is not routinely monitored. Since patients may not tolerate cables attached to their chest, we developed an unobtrusive and contactless measurement method which can be placed under a mattress. The sensor array uses the Maxwell-Wagner relaxation effect by capacitive injection of a high-frequency voltage into the torso and subsequent measurement of respiratory-induced phase shift. Simulations of the entire measurement scenario indicate an improved signal-to-noise ratio if a differential method is applied with specific positioning of the electrodes. A prototype was designed and the simulations were confirmed with measurements on a phantom and in a human self-experiment by the authors using self-constructed hardware. Movement artifacts were detected using an artifact detection algorithm which allows reliable estimation of the respiratory rate.